Keck spectroscopy of five proto-globular cluster candidates in NGC 1275 has been combined with Hubble Space Telescope Wide Field Planetary Camera 2 photometry to explore the nature and origin of these objects and discriminate between merger and cooling-flow scenarios for globular cluster formation. The objects we have studied are not H II regions, but rather star clusters, yet their integrated spectral properties do not resemble young or intermediate-age Magellanic Cloud clusters or Milky Way open clusters. The clusters' Balmer absorption appears to be too strong to be consistent with any of the standard Bruzual & Chariot evolutionary models at any metallicity. If the Bruzual & Chariot models are adopted, an initial mass function (IMF) that is skewed to high masses provides a better fit to the data of the proto-globular cluster candidates. A truncated IMF with a mass range of 2-3 M-. reproduces the observed Balmer equivalent widths and colors at similar to 450 Myr. Formation in a continuous cooling flow appears to be ruled out since the age of the clusters is much larger than the cooling time, the spatial scale of the clusters is much smaller than the cooling-flow radius, and the deduced star formation rate in the cooling flow favors a steep rather than a flat IMF. A merger would have to produce clusters only in the central few kiloparsecs, presumably from gas in the merging galaxies that was channeled rapidly to the center. Widespread shocks in merging galaxies cannot have produced these clusters. If these objects are confirmed to have a relatively flat, or truncated, IMF, it is unclear whether they will evolve into objects that we would regard as bona fide globular clusters.